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Transistors and Digital Logic Gates

Flow and Pressure

To begin this Web Lecture, we will take a brief excursion into electrical
engineering by way of plumbing!

Figure 1. Click to open or close the valve.
See what happens to the pressure.

Consider the apparatus in Figure 1. We have a water reservoir and two large
pipes joined by a smaller, constricted pipe. The upper pipe is connected to the
reservoir and the lower pipe is open. A valve can control flow through the
lower pipe. Two pressure gauges measure the pressure in the pipes.

The reservoir is drawn to fit the page; imagine that its capacity is very
large -- on the order of that of a municipal water system. In other words,
the reservoir will provide water at constant pressure and a high flow rate
for a very long time.

When the valve is closed, the pressure is equal on both sides of the
constriction. Click on the valve wheel to open or close the valve and
observe
what happens to the pressure.

When the valve is open, water escapes from the system through the open lower
pipe, and the pressure in the lower pipe drops because the rate of
supply is limited by the constriction. The pressure above the
constriction remains high because of the reservoir supply. In other words,
there is a pressure drop across the constricted pipe. The pressure
drop occurs only when there is flow through the constriction; when there
is no flow, the pressure is constant throughout.

Electrical Pressure

Electricity has "pressure" just as water does. Electrical pressure, or
electromotive force, is measured in Volts and is often called
voltage. We saw in the previous
web lecture that switches could be used to control the flow of electricity.
The volume of electrical flow is measured in Amperes and is called
current.

A switch is an all-or-nothing device like the valve in Figure 1. There are
devices that can impede the flow of electricity, similar to the constricted
pipe in Figure 1. These are called resistors and they appear as
a sawtooth line in a schematic diagram. The relationship among resistance,
current and voltage is described by Ohm's Law, which we will not
study here.

What is important to students of digital logic is this: If no current is
flowing through a resistor, the voltage at the two ends will be the same;
if current is made to flow through the resistor, there will be a
voltage drop across the resistor. This is analogous to the pressure
drop across the constricted pipe of Figure 1. The pressure drops only
when water is flowing.

Consider an electric circuit that is conceptually similar to
Figure 1.

Figure 2. Click on the switch to change the state of
the circuit.

The circuit of Figure 2. has a switch, a resistor, and two LEDs.
The resistor is shown as a sawtooth line. The symbol
Vcc
indicates the supply voltage. Later we will learn that this supply voltage
is common to the collectors of our transistors, hence the name. The striped
triangle at the bottom of the diagram is the "ground" symbol and indicates
the return to the power source.

In digital logic, it is common to let a "high" voltage, that is a voltage
nearly equal to Vcc indicate a logical one, and a "low" voltage
-- a voltage
near zero -- indicate a logical zero. In the initial state, with the switch
open, both LEDs in Figure 2. are on indicating a logical value of one.

Now click on the switch to close it. Closing the switch allows current to
flow from Vcc to ground. Because current is flowing, there is
a voltage
drop across the resistor. The voltage at the lower end, labeled "Output,"
becomes approximately zero as shown by the extinguished LED. The upper
LED remains on because it is connected to Vcc. In future
circuits, we
will not bother to show the upper LED because it is on all the time.

An important thing to notice about Figure 2. is that the output is true, or
one, when the switch is open. This circuit is an inverter; it
computes the Boolean NOT function.

Transistors as Switches

At last we are ready to start using transistors! A bipolar junction transistor is an
electronic device with three elements called the base, the collector,
and the emitter. Transistors can function as analog devices and are
used in that way in radios, amplifiers, and similar gear. By choosing
suitable transistors and providing suitable inputs, they can also
function as digital devices -- switches that are either on or off.

Transistors have the property that if a suitable voltage is applied to
the base, current can flow between the collector and the
emitter. This is exactly like the mechanical switches we've been using
except that we control the switching action with voltage instead of
mecahnical motion. Switches made in this way can operate at electronic
speeds instead of mechanical speeds. The switching speed of a typical
transistor is a few nanoseconds -- a few billionths of a second. That's
how computers can operate as fast as they do.

Replacing the mechanical switch with a transistor gives the circuit
of Figure 3.

Figure 3. An inverter. Click on the pushbutton to change the voltage
at the base of the transistor.

The circular element in the schematic diagram represents a bipolar
transistor. (Other kinds of transistors can be used in digital
logic; they have different symbols.) The transistor has three connections:
the collector, the emitter, and the base. When the voltage at the base
of the transistor is high enough, current can flow from the collector to
the emitter. When the voltage at the base is near zero, no current can
flow. The transistor acts like a switch.

The pushbutton in the diagram can be used to apply or remove voltage at
the base of the transistor. Click on the pushbutton and observe what
happens. When voltage is present at the base of the transistor, current
flows from collector to emitter, then to ground, and there is a voltage
drop across the resistor. The voltage at the output drops to near zero.
Removing the voltage at the base stops the current flow and the output
voltage rises to be equal to Vcc.

A transistor used in this way is an amplifier as well as a switch. A
voltage lower than Vcc is enough to make the transistor switch
on; very little current flows from the base to ground through the
emitter. A much larger current flows from collector to emitter and
then to ground. The transistor is a current amplifier, but the
important part of the circuit is the voltage change at the output,
from near Vcc when the transistor is switched off to near zero
when
the transistor is switched on.

Like the circuit in Figure 2, this circuit is an inverter. The
output is high when the input is low and vice-versa. This circuit computes
the Boolean NOT function. (If you are troubled by
the lack of a second connection on the pushbutton and the LED, refer to
the section on abstraction
in the previous Web Lecture.)

NAND and NOR Gates

Figure 4. A NAND gate. The value of the
output is controlled by the two inputs A and B.

The circuit of Figure 3 illustrates some important concepts, but it isn't
very interesting.
We can do more if we build circuits with two or more
inputs. Figure 4. shows a NAND gate. The name
NAND is a contraction of not-and.
Current can flow, and produce a voltage drop across the resistor, only
if both transistors are conducting. Having either transistor switched
off is enough to block current flow and hold the output high.

For purposes of this lecture we are going to define a "high" voltage -- a
voltage near Vcc -- to indicate a logical 1, or true. A low
voltage,
near zero will indicate a logical 0, or false. (It is possible to reverse
those definitions so long as one is consistent. We will not study
negative logic circuits here.)

Table 1. NAND

A

B

X

0

0

1

0

1

1

1

0

1

1

1

0

Using 1 to represent a high voltage and 0 for low, we can write a
truth table that describes the behavior of the
NAND gate. Columns A and B of the table represent
the two inputs, A and B, of the NAND gate. The X
column shows what the output will be for each combination of A and B.
The truth table for the Boolean NAND function
appears at the left. Experiment with the circuit in Figure 4 and verify
that it actually computes the NAND function.

It is clear from the schematic diagram that we could build a
NAND gate with more than two inputs. Adding a third
transistor in series gives a three-input NAND. As
an exercise, write the truth table for a three-input NAND
gate. You will have inputs A, B, and C and output X.

Figure 5. A NOR gate. The transistors
are connected in parallel.

The NAND gate has its transistors connected in series.
Recall from the Electric Circuits Web
Lecture that
switches can be connected in series or parallel. If we connect transistors
in parallel as shown in Figure 5, applying a signal to the base of either
transistor is sufficient to allow current to flow through the resistor and
pull the output voltage to near zero. This is the NOR gate.
The name NOR is a contraction of not-or.

Table 2. NOR

A

B

X

0

0

1

0

1

0

1

0

0

1

1

0

Let's look at the truth table for the NOR gate.
Again we have inputs A and B and output X. This time, X is true, or 1,
only when A and B are both 0. Another way of saying that is that X is
1 when neither A nor B is true. Experiment with the circuit to
verify that it computes the function given in Table 2.

As with the NAND gate, the NOR
gate can be extended to more than two inputs by adding more transistors,
this time in parallel.

Figure 5 makes it obvious why the power supply voltage is called
Vcc. It
is connected in parallel, or in common, through the resistor to the
collectors of both transistors. In a complex digital logic circuit, the
same power supply voltage will be connected in common to all the gates.

About now you may be wondering why we started with NAND
and NOR gates instead of the more familiar
AND and OR functions. There
are two reasons, one founded in electrical engineering and one founded in
logic.

Although the gates shown here are simplified by comparison to the actual
construction of integrated circuits, you could go to an electrical
engineering lab and build the circuits of Figures 3, 4, and 5. If you
did, they would function just as the animations demonstrate. These
three gates, NOT, NAND, and
NOR are the simplest possible digital logic gates.
Each has only one transistor per input. Any other gate, and in particular
the non-inverting gates AND and OR
require more transistors.

Even more important is the fact that NAND and
NOR are complete. This means that any
other digital logic gate can be constructed using only
NAND gates or only NOR gates.
A manufacturer of integrated circuits can lay down a pattern of one type
of gate, and then implement any digital logic function by modifying how
the gates are connected.

Digital Logic Symbols

We generally don't draw individual transistors in diagramming digital
logic circuits. Instead we use abstraction to suppress unnecessary detail
and represent only the required information. We need to show three things
about each digital logic gate: the function of the gate, the inputs, and
the output. The
internal construction of the gate and certain connections are suppressed.

Figure 6. Digital Logic Symbols. A.NOT,
B.NAND and C.NOR gates.

Figure 6 shows the symbols for the three digital logic gates we have studied
in this Web Lecture. The function of each gate is represented by
the shape of the symbol. These symbols are variations of the basic
digital logic shapes. The triangle represents an amplifier. Adding a
circle at the output makes it a NOT gate.

The bullet shape is an AND gate; adding the
circle makes it a NAND gate.

The shield shape is an OR gate; with a circle it
becomes a NOR gate.

The inputs are shown as wires at
the left of each gate, and the output is a wire on the right. Real gates
require connections to Vcc and ground in addition to their
inputs and outputs. These connections are
not shown on digital logic symbols, but are assumed to be present. This
is another example of abstraction.

The circle at the output end of each gate is called an inversion bubble.
It indicates that the output is inverted. Table 1 is the truth table for
a NAND gate; each bit of the output is the
complement, or inverse of the corresponding bit for the
AND function. Similarly, the truth table for
NOR shown in Table 2 is the inverse of the
OR function.

We have examined the way three types of digital logic gates are constructed.
In the next Web Lecture we will derive some other types of gates and build
a simple digital logic circuit.